Unbounded Solutions to Systems of Differential Equations at Resonance

Journal of Dynamics and Differential Equations - We deal with a weakly coupled system of ODEs of the type $$\begin{aligned} x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots ,x_d) = p_j(t), \qquad...     

Radiation bursts from particles in the field of compact, impenetrable, astrophysical objects

The radiation emitted by charged, scalar particles in a Schwarzschild field with maximal acceleration corrections is calculated classically and in the tree approximation of quantum field theory. In both instances the particles emit radiation that has characteristics similar to those of gamma-ray bursters.     

Application of the wavelet transform for a channel flow in a mixed convection phenomenon

The aim of this paper is to investigate laminar-turbulent transition in a mixed convection phenomenon occurring in a horizontal rectangular duct. Indeed, laminar-turbulent transition is well known in the case of forced convection but the presence of secondary flow induced by natural convection on this transition is not well highlighted. In this study, we will not be concerned by determining a critical threshold value of a Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of a mixed convection phenomenon. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for various experimental conditions allows the degree of turbulence to be measured. The variation of the Hölder exponent versus heat flux and Reynolds number enables us to show that there are two ways to go towards turbulence: thermal by increasing heat flux and hydrodynamic by increasing fluid velocity.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

Analysis of egg-based model wall paintings by use of an innovative combined dot-ELISA and UPLC-based approach

The chemical analysis of egg-based wall paintings—the mezzo fresco technique—is an interesting topic in the characterisation of organic binders. A revised procedure for a dot-enzyme-linked immunosorbent assay (dot-ELISA) able to detect protein components of egg-based wall paintings is reported. In the new dot-ELISA procedure we succeeded in maximizing the staining colour by adjusting the temperature during the staining reaction. Quantification of the colour intensity by visible reflectance spectroscopy resulted in a straight line plot of protein concentration against reflectance in the wavelength range 380–780 nm. The modified dot-ELISA procedure is proposed as a semi-quantitative analytical method for characterisation of protein binders in egg-based paintings. To evaluate its performance, the method was first applied to standard samples (ovalbumin, whole egg, egg white), then to model specimens, and finally to real samples (Giotto’s wall paintings). Moreover, amino acid analysis performed by innovative ultra-performance liquid chromatography was applied both to standards and to model samples and the results were compared with those from the dot-ELISA tests. In particular, after protein hydrolysis (24 h, 114 °C, 6 mol L^?1 HCl) of the samples, amino acid derivatization by use of 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate enabled reproducible analysis of amino acids. This UPLC amino acid analysis was rapid and reproducible and was applied for the first time to egg-based paintings. Because the painting technique involved the use of egg-based tempera on fresh lime-based mortar, the study enabled investigation of the effect of the alkaline environment on egg-protein detection by both methods.

Quantitation of a de‐fluorinated analogue of Casopitant Mesylate by normal‐phase liquid chromatography/mass spectrometry

The introduction of Quality by Design (QbD) in Drug Development has resulted in a greater emphasis on chemical process understanding, in particular on the origin and fate of impurities. Therefore, the identification and quantitation of low level impurities in new Active Pharmaceutical Ingredients (APIs) play a crucial role in project progression and this has created a greater need for sensitive and selective analytical methodology. Consequently, scientists are constantly challenged to look for new applications of traditional analytical techniques. In this context a normal‐phase liquid chromatography/electrospray ionization mass spectrometry (LC/ESI‐MS) method was developed to determine the amount of a de‐fluorinated analogue impurity in Casopitant Mesylate, a new API under development in GlaxoSmithKline, Verona. Normal‐phase LC provided the selectivity needed between our target analyte and Casopitant, while a single quadrupole mass spectrometer was used to ensure the sensitivity needed to detect the impurity at <0.05%w/w. Standard solutions and samples were prepared in heptane/ethanol (50:50, v/v) containing 1% of 2 M NH₃ in ethanol; the mobile phase consisted of heptane/ethanol (95:5, v/v) with isocratic elution (flow rate: 1.0 mL/min, total run time: 23 min). To allow the formation of ions in solutions under normal‐phase (apolar) conditions, a post‐column infusion of a solution of 0.1% v/v of formic acid in methanol was applied (flow rate: 200 µL/min). The analysis was carried out in positive ion mode, monitoring the impurity by single ion monitoring (SIM). The method was fully validated and its applicability was demonstrated by the analysis of real‐life samples. This work is an example of the need for selective and accurate methodology during the development of a new chemical entity in order to develop an appropriate control strategy for impurities to ultimately ensure patient safety. Copyright © 2010 John Wiley & Sons, Ltd.     

A Geometric formulation of the causal Interpretation of quantum mechanics

The principles of the causal interpretation are embodied in a conformally invariant theory in Weyl space. The particle is represented by a spherically symmetric thin-shell solution to Einstein's equations. Use of the Gauss-Mainardi-Codazzi formalism yields new insights into the issues of nonlocality, the quantum potential, and the guidance mechanism.1. The issue of negative probabilities associated with second-order wave equations in the causal interpretation is discussed in Ref. 19.     

Synthetic peptides in the diagnosis of HIV infection

Peptide-based enzyme-linked immunosorbent assays have been found to be enough sensitive and specific for the diagnosis of human immunodeficiency virus specific antibodies in acquired immunodeficiency syndrome patients. This review provides an overview of the most important peptides developed for use as synthetic antigens in immunodiagnosis of HIV-infected patients. In particular, many studies have been devoted to discriminate between the two retroviruses HIV-1 and HIV-2, as well as different subtypes.